Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.
Features & Benefits
- Proof techniques and strategies are thoroughly discussed and the underlying logic behind them is made transparent.
- Each chapter section begins with a set of guided reading questions intended to help students to identify the most significant points made within the section.
- Practice problems are embedded within chapters so that students can actively work with a key idea that has just been introduced.
- Each chapter also includes a collection of problems, ranging in level of difficulty, which are perfect for in-class discussion or homework assignments.
Chapter 1 Mathematics and Mathematical Activity
Chapter 2 Sets, Numbers, and Axioms
Chapter 3 Elementary Logic
Chapter 4 Planning and Writing Proofs
Chapter 5 Relations and Functions
Chapter 6 The Natural Numbers, Induction, and Counting
Chapter 7 Further Mathematical Explorations
Michael J Cullinane, PhD-Professor of Mathematics, Keene State University, Keene, New Hampshire